Video displays using cathode-ray tubes (CRTs) are widely used. A voltage applied to the CRT determines the intensity or brightness of a pixel. As the applied voltage is increased, the pixel appears brighter as the CRT's light output increases. However, the relationship of the applied voltage to the light output is not a simple linear function. Instead, the light output is proportional to the applied voltage raised to a power of a constant gamma (γ):L=vγwhere v is the applied or driving voltage normalized between 0 and 1 and L is the light output. For television monitors, gamma γ is typically between 2.2 to 2.8, while gamma is somewhat lower, between 1.4 and 2.2, for most computer monitors. Thus the light output is roughly the square of the normalized voltage.
A captured image, such as one captured by a sensors in a digital camera, may be corrected for this non-linear relationship of light and voltage. The red, green, and blue (R, G, B) components of a pixel may each be separately corrected. This correction uses a gamma-correction function that is complementary to the distortion function (above). The uncorrected captured pixel w is gamma-corrected to generate corrected pixel w′ using the following equation:w″=wαwhere α is the reciprocal of gamma, 1/γ.
Many methods for gamma correction are known, both using analog and using digital techniques. For computer and digital camera systems, digital techniques are preferred since they are easier to integrate with the other digital functions.
Power functions such as the gamma-correction function have a special kind of symmetry that can be used to simplify implementation of the function. This symmetry depends on ratios. FIG. 1 shows a graph of a gamma-correction function that is divided into segments that are ratios of each other.
The gamma function graph has an input shown on the x axis that is normalized to be between 0 and 1. The output of the function is the y value of the curve at any desired x value. The y value can be read from the y axis. The curve for a power function such as a gamma correction function has the general curved shape shown.
The function curve is divided into several segments X0, X1, X2 . . . X5. The largest segment X0 is on the right and covers input x values from 0.5 to 1. The next segment X1 is half the width of segment X0, having inputs from 0.25 to 0.5. The third segment X2 is even smaller in width, having inputs from 0.125 to 0.25. Each successive segment has one-half the width of the segment to its right. The last (leftmost) segment X5 spans the range of 0 to 1/64.
The segments are thus related to each other by a ratio relationship. The segments are ratio-metrically related. The gamma function is a self-similar function because the function curve is similar in each of the segments. The function curve within each segment can be approximated as a straight line so that the gamma correction function is approximated as a piece-wise-linear (PWL) function. A non-linear correction can also be added to the PWL function. See U.S. Pat. No. 5,408,267 Main and assigned to The 3DO Company of Redwood City, Calif.